Turkish Journal of Mathematics
Abstract
We establish necessary and sufficient conditions on a weight v governing the trace inequality \hat{K}f _{L^q_v(\hat{E})} \leq C f _{L^p(E)}, where E is a cone on a homogeneous group, \hat{E}: = E \times R_+ and \hat{K} is a positive kernel operator defined on \hat{E}. Compactness criteria for this operator are also established.
DOI
10.3906/mat-1209-21
Keywords
Operators with positive kernels, upper half-space, potentials, homogeneous groups, trace inequality, boundedness, compactness, weights
First Page
119
Last Page
135
Recommended Citation
ASHRAF, U, ASIF, M, & MESKHI, A (2014). Kernel operators on the upper half-space: boundedness and compactness criteria. Turkish Journal of Mathematics 38 (1): 119-135. https://doi.org/10.3906/mat-1209-21
